Some Very Special Angles :)

This week I learned the sine and cosine values of special angles.  The special angles are 30˚ ,45˚,& 60˚

 degrees.  π/6 = 30˚ , π/6 = 60˚ , π/4 = 45˚.  These special angles are in each quadrant.  Sin represents the

 y and cosine represents the x. 

The sin and cosine (cos) have +/- values depending on the quadrant they are in. 

Quad  I:  +sin & +cos

Quad II:  +sin & -cos 

Quad III:  -sin & -cos 

Quad IV:  -sin & +cos

The special values are

sin π/6 or 30˚=1/2                            cos  π/6 or 30˚= √3/2

sin  π/6 or 60˚ = √3/2                       cos π/6 or 60˚ = 1/2

sin  π/4 or 45˚ =  √2/2                      cos  π/4 =or  45˚ = √2/2

1)     1.  Find sin 150˚.

First determine the quadrant, which is Q II and makes the sin +.  Then subtract 150 from 180 to find the reference angle, you get 30˚.  So sin 150˚=+1/2.

2)    2.  Find cos 7π/6.

First determine the quadrant, which is Q III and makes the cos -. Then subtract π from 7π/6 to find the reference angle, you get π/6.  So cos 7π/6 = √3/2.

Jenna Roussel